Geodesic
A result on hermitian operators
Glasgow mathematical journal, Tome 31 (1989) no. 1, pp. 71-72

Voir la notice de l'article provenant de la source Cambridge University Press

Let X be a complex Banach space. For any bounded linear operator T on X, the (spatial) numerical range of T is denned as the setIf V(T) ⊆ R, then T is called hermitian. Vidav and Palmer (see Theorem 6 of [3, p. 78] proved that if the set {H + iK:H and K are hermitian} contains all operators, then X is a Hilbert space. It is natural to ask the following question. 
Jamison, J. E.; Lin, Pei-Kee. A result on hermitian operators. Glasgow mathematical journal, Tome 31 (1989) no. 1, pp. 71-72. doi: 10.1017/S0017089500007564
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